As Labour MP Lisa Nandy told Business Insider on the eve of the annual get together, the argument about Corbyn’s leadership was “effectively over.”

However, while there is no doubting Labour is in its best shape for years, a big debate is brewing beneath the surface that threatens to split the party right down the middle — should Brexit mean leaving the single market?

As the party’s chief elections strategist, Andrew Gwynne, told a fringe event this week, it’s a question that could tear the party apart. That’s because it’s not just a question about Britain’s future with an EU institution — it’s much more than that. For Labour MPs, it’s a question of Labour values, and how Labour politics ought to be applied in 2017.

This was clear in remarks exchanged by MPs Alison McGovern, who wants to stay in the single market, and Kelvin Hopkins, one of the few Labour leavers (also known as “Lexiteers”) in a fringe hosted be Open Britain on Tuesday. McGovern suggested leaving the single market would mean “finishing what Thatcher started,” while Hopkins portrayed the EU as a Thatcherite regime, describing it as a “neoliberal construct that ought to be challenged.”

McGovern inhabits a wing of the party alongside MPs like Chuka Umunna, Heidi Alexander, Stephen Kinnock and others who are urging Corbyn to make remaining in the single market party policy. Labour Brexiteers like Hopkins belong to a much smaller club. However, a much larger number of Labour MPs represent Leave-voting constituencies. And for many of those MPs, the prospect of staying in the single market, and the likelihood of accepting the free movement of people by virtue of that commitment, is one that makes them increasingly anxious.

The progressive dilemma

For Alexander, MP for the London constituency of Lewisham East, Labour simply will not be able to deliver the policies promised in its progressive election manifesto if Britain leaves the single market as part of its exit from the EU. It’s not sustainable,” she told BI in Brighton.

“If you look at the analysis that was done by the Treasury before the referendum, they set out a number of different scenarios and what the impact on the public finances would be. We are in the world of least damaging options.

“That analysis in February 2016 suggested that an EEA system would hit public finances around £20 billion over 15 years; a Canadian style free trade deal would hit public finances by £36 billion; crashing out on WTO terms would mean £45 billion in potential impact. £45 billion is the equivalent of five teams of annual spending on GPs. It’s the same as three times annual local authority expenditure on social care.”

She added: “I don’t think you can afford an anti-austerity agenda if you’re not in the single market.”

Kinnock made the same point, describing it as the “600lb gorilla in the room” when he spoke to BI.

He explained: “You can have all of the very progressive, radical policies that you like in your manifesto, but if the fundamentals of your economy are going to hit the wall, then it just isn’t sustainable,” the MP for Aberavon said.

Hopkins shrugged off these concerns at the Open Britain fringe. “Where are the jobs going to be lost? I don’t see where they are going to be lost [from leaving the single market]” he said, while McGovern and Umunna looked at each other in disbelief.

The MP for Luton North made the case for why leaving the single market is progressive, claiming that being a member makes it more difficult for state governments to nationalise industries, and imposes restrictions on state aid. Corbyn expressed these worries himself in interviews last weekend. Labour’s single market backers dismiss this, with Umunna describing them as “complete nonsense.”

The EEA question

Alexander has taken the fight for the single market to the House of Commons. The former shadow health secretary has tabled an amendment to the EU Withdrawal Bill calling on the government to give Parliament a vote on whether Britain should leave the European Economic Area (EEA). The Bill’s third reading will take place later this year.

The EEA, which Britain is a member of, allows Norway, Lichenstein and Iceland to participate fully in the single market despite not being in the EU. Alexander, Kinnock and others argue that Britain’s membership of the EEA is separate to its EU membership, and that government must get parliamentary approval before taking Britain out of the former. By staying in the EEA would beyond Brexit day Britain would, in theory, stay in the single market.

Alexander is confident the amendment has the potential to attract a significant amount of cross-party support. “I’ve spoken to a number of Conservative MPs who are interested in the whole idea of the single market and EEA,” she said.

“There is a fundamental democratic question at stake here. We had Article 50 triggered on the back of a full act of parliament. Coming out of the EEA is separate from the EU. If the government wishes to take the UK out of the EEA, it’s MPs who should determine that and not David Davis behind his desk in Westminster. Under the EU Withdrawal bill, there is nothing to stop a minister deciding to trigger Article 127 of the EEA Agreement and take us out of the EEA. I think that’s fundamentally wrong.”

Kinnock, who is one of to the amendment’s supporters, told BI that the Gina Miller case “established legal precedent” which means Prime Minister May has no choice but to give MPs a vote before taking Britain out of the EEA.

He added: “The big question here is that what are those pro-EU Tories willing to do? How far are they prepared to go? I can absolutely understand how difficult it is for them but they’re going to have to make a decision.

Immigration, immigration, immigration

Umunna told the Open Britain fringe that the pro-single market movement has in recent months become more organised and developed a more coherent message. This is undoubtedly true. But even within this internal Labour grouping, there is a fundamental disagreement over a key aspect of the single market debate: immigration.

“This is perhaps where I diverge to some extent,” Kinnock said. Kinnock, a newly-appointed member of the Brexit committee, believes one of the biggest advantages of the EEA model is it offers the possibility of imposing emergency breaks on any of the single market’s four freedoms, including the free movement of people.

“Why is it we believe in regulating the banks and not regulating the inward flow of labour from the EU?” he added.

“It’s a market like any other market and it needs to be regulated. We also need to think about how many communities have felt left behind by globalisation that we are elected to represent.

“I know that colleagues say there is a lot more we can do within current EU regulations to limit inward migration, but these measures are too far downstream. We need an upstream approach to regulating free movement. We are a whole nation party and the views on this issue in the big metropolitan cities is a lot to different to in places like my constituency.”

Alexander, in her own words, takes a different view. “I don’t believe we should be sacrificing our economy on the altar of concerns about immigration,” she told BI.

“I’m also concerned that the debate about immigration has been misleading over the last few years in the UK. We control immigration from countries which account for 90% of the world’s population. We have a more relaxed for 10% that live within the EU. Now, instead of immediately accepting the argument that we have to curb immigration, we need to think about the costs of decreasing the number of EU migrants who come here.

Keir Starmer’s announcement that a Labour government would keep Britain in the single market during transitional period suggests that the pro-single market position is winning for now. “That side of the debate is certainly making a lot of noise and is getting lots of traction,” Kinnock said.

But even though support for retaining close trading ties with Europe is growing within Labour, the question of what to do about immigration remains hanging in the air, even among the party’s biggest supporters of the single market.